STA 2016 Final Project Code
Bushra Haque
2024-12-24
## ℹ <https://maps.googleapis.com/maps/api/geocode/json?address=CN+Tower,+Toronto&key=xxx>## ℹ <https://maps.googleapis.com/maps/api/geocode/json?address=Royal+Ontario+Museum,+Toronto&key=xxx>## ℹ <https://maps.googleapis.com/maps/api/geocode/json?address=Ripley's+Aquarium+of+Canada,+Toronto&key=xxx>## ℹ <https://maps.googleapis.com/maps/api/geocode/json?address=Distillery+Historic+District,+Toronto&key=xxx>## ℹ <https://maps.googleapis.com/maps/api/geocode/json?address=Art+Gallery+of+Ontario,+Toronto&key=xxx>## ℹ <https://maps.googleapis.com/maps/api/geocode/json?address=Casa+Loma,+Toronto&key=xxx>## ℹ <https://maps.googleapis.com/maps/api/geocode/json?address=Toronto+Islands,+Toronto&key=xxx>## ℹ <https://maps.googleapis.com/maps/api/geocode/json?address=St.+Lawrence+Market,+Toronto&key=xxx>## ℹ <https://maps.googleapis.com/maps/api/geocode/json?address=Hockey+Hall+of+Fame,+Toronto&key=xxx>## ℹ <https://maps.googleapis.com/maps/api/geocode/json?address=Nathan+Phillips+Square,+Toronto&key=xxx>Base Map of Sept. Avg Price
Adjacency Matrices & Weights
Why we might want distance over contiguity based?
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.09091 0.14286 0.16667 0.16746 0.20000 0.33333## Warning: st_centroid assumes attributes are constant over geometries
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3333 0.3333 0.3333 0.3333 0.3333 0.3333
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667## Warning in knn2nb(knearneigh(coords, k = 1)): neighbour object has 41
## sub-graphs
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.06250 0.08333 0.10000 0.14799 0.16667 1.00000Global Moran’s I
This will give a general statistic for the entire study area. We pick fixed distance with row standardization.
## weight.matrix moran.I expectation variance p.value
## 1 Queen 0.2138924 -0.007194245 0.002386915 3.015996e-06
## 2 kNN3 0.1874309 -0.007194245 0.004072117 1.144503e-03
## 3 kNN6 0.1421564 -0.007194245 0.002044641 4.784123e-04
## 4 IDW 0.2170340 -0.007194245 0.002980003 1.999467e-05## idw.weights moran.I expectation variance p.value
## 1 Row Standardized 0.2170340 -0.007194245 0.002980003 1.999467e-05
## 2 Binary 0.1433354 -0.007194245 0.001945729 3.217730e-04If you’re analyzing Airbnb data in Toronto:
- Positive Moran’s I at short lags might indicate clustering of high-priced listings in affluent neighborhoods.
- A transition to negative Moran’s I at intermediate lags could suggest competition among listings or distinct pricing zones.
- Moran’s I near zero at larger lags suggests no meaningful relationship beyond a certain distance, potentially due to unrelated neighborhood effects.
MCMC + Permutation
Similar p-value + significant.
##
## Monte-Carlo simulation of Moran I
##
## data: nbhd$avg_sept_price
## weights: dist1.wts
## number of simulations + 1: 10000
##
## statistic = 0.21703, observed rank = 9984, p-value = 0.0016
## alternative hypothesis: greater
Local Moran’s I
##
## Low-Low High-Low Low-High High-High
## 51 15 30 44Local Getis’ Ord
Model Fitting
Linear
##
## Call:
## lm(formula = avg_sept_price ~ n_sept_listings + n_listings_near_subway +
## median_income, data = nbhd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -112.41 -22.36 -10.27 14.23 389.68
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 40.9350720 17.5811875 2.328 0.0214 *
## n_sept_listings -0.1557997 0.1231602 -1.265 0.2080
## n_listings_near_subway 0.1930344 0.1210305 1.595 0.1131
## median_income 0.0007068 0.0001333 5.304 4.48e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 52.25 on 136 degrees of freedom
## Multiple R-squared: 0.2553, Adjusted R-squared: 0.2389
## F-statistic: 15.54 on 3 and 136 DF, p-value: 9.528e-09##
## Moran I test under randomisation
##
## data: nbhd$lm_resid
## weights: dist1.wts
##
## Moran I statistic standard deviate = 2.0751, p-value = 0.01899
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## 0.095187757 -0.007194245 0.002434230SAR Spatial Error
##
## Call:
## spautolm(formula = avg_sept_price ~ n_sept_listings + n_listings_near_subway +
## median_income, data = nbhd, listw = dist1.wts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -100.8202 -22.3484 -9.3946 12.9395 388.1777
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 42.62153524 18.28459493 2.3310 0.01975
## n_sept_listings -0.16192243 0.12678158 -1.2772 0.20154
## n_listings_near_subway 0.19576441 0.12529522 1.5624 0.11819
## median_income 0.00069719 0.00013861 5.0299 4.908e-07
##
## Lambda: 0.18677 LR test value: 2.5338 p-value: 0.11143
## Numerical Hessian standard error of lambda: 0.11512
##
## Log likelihood: -749.1896
## ML residual variance (sigma squared): 2585.6, (sigma: 50.848)
## Number of observations: 140
## Number of parameters estimated: 6
## AIC: 1510.4##
## Moran I test under randomisation
##
## data: nbhd$sar_err_resid
## weights: dist1.wts
##
## Moran I statistic standard deviate = 0.10918, p-value = 0.4565
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## -0.001834502 -0.007194245 0.002409946SAR Spatial Lag
##
## Call:
## lagsarlm(formula = avg_sept_price ~ n_sept_listings + n_listings_near_subway +
## median_income, data = nbhd, listw = dist1.wts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -96.5218 -22.2672 -9.6825 11.4059 390.3965
##
## Type: lag
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 24.21027309 19.80738113 1.2223 0.2216
## n_sept_listings -0.11753964 0.12208107 -0.9628 0.3356
## n_listings_near_subway 0.15180256 0.12021029 1.2628 0.2067
## median_income 0.00064917 0.00013454 4.8252 1.398e-06
##
## Rho: 0.18443, LR test value: 2.8662, p-value: 0.090456
## Asymptotic standard error: 0.11103
## z-value: 1.6611, p-value: 0.09669
## Wald statistic: 2.7593, p-value: 0.09669
##
## Log likelihood: -749.0234 for lag model
## ML residual variance (sigma squared): 2579.9, (sigma: 50.793)
## Number of observations: 140
## Number of parameters estimated: 6
## AIC: 1510, (AIC for lm: 1510.9)
## LM test for residual autocorrelation
## test value: 0.0013941, p-value: 0.97022##
## Moran I test under randomisation
##
## data: nbhd$sar_lag_resid
## weights: dist1.wts
##
## Moran I statistic standard deviate = 0.13041, p-value = 0.4481
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## -0.0008106219 -0.0071942446 0.0023961264SAR Spatial Lag + Error
##
## Call:
## sacsarlm(formula = avg_sept_price ~ n_sept_listings + n_listings_near_subway,
## data = nbhd, listw = dist1.wts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -71.792 -28.269 -10.020 14.003 367.884
##
## Type: sac
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 77.73725 38.20353 2.0348 0.04187
## n_sept_listings -0.23849 0.13776 -1.7311 0.08343
## n_listings_near_subway 0.26691 0.13809 1.9329 0.05325
##
## Rho: 0.39544
## Asymptotic standard error: 0.29206
## z-value: 1.354, p-value: 0.17574
## Lambda: -0.12722
## Asymptotic standard error: 0.37831
## z-value: -0.3363, p-value: 0.73665
##
## LR test value: 7.2499, p-value: 0.02665
##
## Log likelihood: -759.9923 for sac model
## ML residual variance (sigma squared): 2926.8, (sigma: 54.1)
## Number of observations: 140
## Number of parameters estimated: 6
## AIC: 1532, (AIC for lm: 1535.2)##
## Moran I test under randomisation
##
## data: nbhd$sar_lag_err_resid
## weights: dist1.wts
##
## Moran I statistic standard deviate = 0.13808, p-value = 0.4451
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## -0.000303365 -0.007194245 0.002490436CAR
## Warning in spautolm(avg_sept_price ~ n_sept_listings + n_listings_near_subway,
## : Non-symmetric spatial weights in CAR model##
## Call:
## spautolm(formula = avg_sept_price ~ n_sept_listings + n_listings_near_subway,
## data = nbhd, listw = dist1.wts, family = "CAR")
##
## Residuals:
## Min 1Q Median 3Q Max
## -76.162 -29.414 -8.703 14.566 363.323
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 132.58890 7.94417 16.6901 < 2.2e-16
## n_sept_listings -0.39248 0.13800 -2.8441 0.004453
## n_listings_near_subway 0.41018 0.13676 2.9993 0.002706
##
## Lambda: 0.5133 LR test value: 6.0853 p-value: 0.013631
## Numerical Hessian standard error of lambda: 0.19776
##
## Log likelihood: -760.5746
## ML residual variance (sigma squared): 2971.4, (sigma: 54.511)
## Number of observations: 140
## Number of parameters estimated: 5
## AIC: 1531.1##
## Moran I test under randomisation
##
## data: nbhd$car_resid
## weights: dist1.wts
##
## Moran I statistic standard deviate = -2.0092, p-value = 0.9777
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## -0.108456646 -0.007194245 0.002540168